Lake Shore Cryotronics Measure Ready M91 FastHall, User Manual

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Several other unwanted voltages depend on the sample temperature, temperature
gradients and magnetic field. Many can be eliminated by a combination of current
and field reversal, but others cannot. One example that cannot be eliminated in one
of these ways is the Ettingshausen effect voltage (section 1.5.5.4.1).
1.5.5.4.1 Ettingshausen Effect Voltage (V
E
)
Even if no external transverse temperature gradient exists, the sample can set up its
own. The Lorentz force shunts slow (cool) and fast (hot) electrons to the sides in
different numbers and causes an internally generated thermoelectric voltage. This
phenomenon is known as the Ettinghausen effect. V
E
is proportional to both current
and magnetic field.
This voltage is also present in the final measured voltage. The M91 measures the sum
of the Hall voltage and the Ettingshausen effect voltage. The user must determine if
the Ettingshausen voltage is small for their samples.
1.5.5.5 Geometry Averaging
Measurement uncertainty can result if a sample is not homogeneous. By definition,
for a homogeneous sample, the voltage V
ij,kl
that is measured is equal to the voltage
V
kl,ij
measured with the current and voltage leads interchanged. For non-
homogeneous samples, the best approximation that can be made is to average these
two voltages. In Hall measurements, this is called geometry averaging. It is
implemented in both Hall voltage and resistivity measurements. The exact
implementation is dependent on the sample structure (section 1.5.5.1). Geometry
averaging is available via the M91 and MeasureLINK™-MCS software.
1.5.5.6 Measurement Averaging
Measurement averaging is available via the MeasureLINK™-MCS software.
Measurement averaging averages individual measurements used in the derivation of
Hall measurement results. It can reduce uncertainty and improve resolution by
rejecting environmental noise, system noise, and sample noise. The improvement
depends on the signal-to-noise ratio of the measurement configuration, and the
number of samples averaged. Averaging more samples requires longer measurement
time.
1.5.6 Van der Pauw
Samples The van der Pauw structure is probably the most popular Hall measurement
structure, primarily because it requires fewer geometrical measurements of the
sample. In 1958, van der Pauw
1 solved the general problem of the potential in a thin
conducting layer of arbitrary shape. His solution allowed resistivity measurements to
be made on any sample of uniform thickness, provided that the sample was
homogeneous and there were no physical holes in it. All that is needed to calculate
sheet resistivity or carrier concentration is four point contacts on the edge of the
surface (or four line contacts on the periphery); an additional measurement of sample
thickness allows calculation of volume resistivity. These relaxed requirements on
sample shape simplify fabrication and measurement in comparison to Hall bar
techniques.
1. Van der Pauw, L. J., "A method of measuring specific resistivity and Hall effect of discs of arbitrary
shape", Philips Res. Reports, 13,1–9 (1958).